My teacher takes off points for significant figure mistakes, but advises us to keep a few extra significant figures until the end. How would I do this problem: Compute the velocity of the Sun around the Milky Way. Assume a circular orbit. Use the values given by Croswell for distance from galactic center and orbital period. Use unit conversions in Appendix A in Hester. Distance of Sun to Center of Galaxy as given by Croswell = 27,000 ly Period of the Sun’s orbit around the Galaxy as given by Croswell = 230,000,000 years 1 ly = 9.4605 * 10^15 m as given by Hester 1 yr = 3.15581 * 10^7s as given by Hester Distance of Sun to Center of Galaxy = 9.4605 * 10^15 * 27,000 = 2.554335 * 10^20 m Circumference of Sun’s orbit around the galaxy = 2 π r Circumference of Sun’s orbit around the galaxy = 2 π 2. 554335 * 10^20 m Circumference of Sun’s orbit around the galaxy = 1.60493601416146 * 10^21 m Period of Sun’s orbit in seconds = s/yr * Pyears Period of Sun’s orbit in seconds = 3.15581 * 10^7s/yr * 2.3 * 10^8 yr Period of Sun’s orbit in seconds = 7.258363 * 10^15 s V = d/t V = 1.60493601416146 * 10^21 m / 7.258363 * 10^15 s V =221115.424257709 m / s V = 221.115424257709 km / s I haven't dumped any figures yet, simply pasting the results out of my calculator. But the 27000 light years confuses me. Is this only 2 significant figures, since I imagine the center of the galaxy isn't exactly 27000 ly, but probably somewhere inbetwen 26500 and 27500. And what if it were known that the center of the galaxy was exactly 27000 light years away. How would that be indicated? 27000.0? And should I be dumping insignificant figures in the intermediate steps? Or only for the final answer? If you were a teacher that marked off for significant figures, how would you want me to do the above problem?